A natural neighbour method based on Fraeijs de Veubeke variational principle for materially non-linear problems

Acta Mechanica Sinica/Lixue Xuebao

Volumn 25, Issue 1, 2009, Pages 83-93

  Li, Xiang ^a   Cescotto, Serge ^b   Rossi, Barbara ^b  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Discretization; Fraeijs de Veubeke variational principle; Meshless method; Natural neighbour method; Voronoi cell

Indexed keywords

BOUNDARY CONDITIONS;

DISCRETIZATION; FRAEIJS DE VEUBEKE VARIATIONAL PRINCIPLE; MESHLESS METHOD; NATURAL NEIGHBOUR METHOD; VORONOI CELL;

VARIATIONAL TECHNIQUES;

EID: 59249093176     PISSN: 05677718     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10409-008-0200-z     Document Type: Article

References (30)

1. E. Cuteo N. Sukumar B. Calvo J. Cegonino M. Doblare 2003 Overview and recent advances in natural neighbour Galerkin methods Arch. Comput. Methods Eng. 10 4 307 384
2. J. Yoo B. Moran J.S. Chen 2004 Stabilized conforming nodal integration in the natural element method Int. J. Numer. Methods Eng. 60 861 890
3. N. Sukumar B. Moran Y. Semenov B. Belikov 2001 Natural neighbor Galerkin methods Int. J. Numer. Methods Eng. 50 1 27
4. N. Sukumar B. Moran T.B. Belytschko 1998 The natural element method in solid mechanics Int. J. Numer. Methods Eng. 43 839 887
5. Lancaster P., Salkauskas K.: Curve and surface fitting: an introduction. Academic Press, London (1990)
6. S.N. Atluri H.G. Kim J.Y. Cho 1999 A critical assessment of the truly meshless local Petrov-Galerkin and local boundary integral equation methods Comput. Mech. 24 348 372
7. S.N. Atluri T. Zhu 2000 New concepts in meshless methods Int. J. Numer. Methods Eng. 47 537 556
8. J.S. Chen C.T. Wu S. Yoon Y. You 2001 A stabilized conforming nodal integration for Galerkin mesh-free methods Int. J. Numer. Methods Eng. 50 435 466
9. J. Yvonnet D. Ryckelynck Ph. Lorong F. Chinesta 2004 A new extension of the natural element method for non-convex and discontinuous domains: the constrained natural element method (c-nem) Int. J. Numer. Methods Eng. 60 1451 1474
10. Yvonnet, J.: Nouvelles approches sans maillage basées sur la méthode des éléments naturels pour la simulation numérique des procédés de mise en forme. [Ph.D. Thesis], Ecole Nationale Supérieure d'Arts et Métiers (2004)
11. D. Gonzalez E. Cueto M.A. Martinez M. Doblare 2004 Numerical integration in natural neighbour Galerkin methods Int. J. Numer. Methods Eng. 60 2077 2104
12. Yagawa, G., Matsubara, H.: Enriched element method and its application to solid mechanics. In: Computational methods in Engineering and Science 2006, pp. 15-18. Proc. EPMESC X, Aug. 21-23, Tsinghua University Press, Springer
13. B. Nayroles G. Touzot P. Villon 1992 Generalizing the finite element method: diffuse approximation and diffuse elements J. Comput. Mech. 10 307 318
14. Y. Kronghauz T. Belytchko 1996 Enforcement of essential boundary conditions in meshless approximations using finite elements Comput. Methods Appl. Mech. Eng. 131 133 145
15. T. Belytchko L. Gu Y.Y. Lu 1994 Fracture and crack growth by element free Galerkin methods Model. Simul. Mater. Sci. Eng. 2 519 534
16. L. Gavette J.J. Benito S. Falcon A. Ruiz 2000 Penalty functions in constrained variational principles for element free Galerkin method Eur. J. Mech. A/Solids 19 699 720
17. T. Belytchko Y.Y. Lu L. Gu 1994 Element-free Galerkin methods Int. J. Numer. Methods Eng. 37 229 256
18. Y.Y. Lu T. Belytchko L. Gu 1994 A new implementation of the element-free Galerkin method Comput. Methods Appl. Mech. Eng. 113 397 414
19. I. Kaljevic S. Saigal 1997 An improved element-free Galerkin formulation Int. J. Numer. Methods Eng. 40 2953 2974
20. S. Ghosh S. Moorthy 1998 Particle fracture simulation in non-uniform microstructures of metal-matrix composites Acta Mater. 46 965 982
21. S. Moorthy S. Ghosh 1998 A Voronoi cell finite element model for particle cracking in elastic-plastic composite materials Comput. Methods Appl. Mech. Eng. 151 377 400
22. C. Hu J. Bai S. Ghosh 2007 Micromechanical and macroscopic models of ductile fracture in particle reinforced metallic materials Model. Simul. Mater. Sci. Eng. 15 4 5377 5392
23. H.W. Zhang H. Wang B.S. Chen Z.Q. Xie 2008 Analysis of Cosserat materials with Voronoi cell finite element method and parametric variational principle Comput. Methods Appl. Mech. Eng. 197 741 755
24. L. Vu-Quoc X.G. Tan 2003 Optimal solid shells for non-linear analyses of multilayer composites I. Statics. Comput. Methods Appl. Mech. Eng. 192 975 1016
25. Herrmann, L.R., Roms, R.M.: A reformulation of the elastic field equations in terms of displacements valid for all admissible values of Poisson's ratio. Trans. ASME, Int. J. Appl. Mech. 140-141 (1964)
26. Fraeijs de Veubeke, B. M.: Diffusion des inconnues hyperstatiques dans les voilures à longerons couplés. Bull. Serv. Technique de l'Aéronautique N° 24, Imprimerie Marcel Hayez, Bruxelles, 56 (1951)
27. V.V. Belikov V.D. Ivanov V.K. Kontorovich S.A. Korytnik A.Y. Semonov 1997 The non Sibsonian interpolation: a new method of interpolation of the values of a function on an arbitrary set of points Comput. Math. Math. Physics 37 1 9 15
28. H. Hiyoshi K. Sugihara 1999 Two generations of an interpolant based on Voronoi diagrams Int. J. Shape Modelling 5 2 219 231
29. R. Sibson 1980 A vector identity for the Dirichlet tessellation Math. Proc. Camb. Philos. Soc. 87 151 155
30. Rossi, B., Pascon, F., Habraken, A.M.: Theoretical and numerical evaluation of residual stresses in thin-walled sections, Report N° AG2007-02/01, ArGEnCo Department, Division of Mechanics of Solids, Fluids and Structures (2007)